Mutual Funds and Management Styles. Active Portfolio Management

Transcription

1 utual Funds and anagement Styles ctve Portfolo anagement ctve Portfolo anagement What s actve portfolo management? How can we measure the contrbuton of actve portfolo management? We start out wth the CP as an equlbrum model f [ E( r r ] E( r ) r β ) The CP dentfes the securty market lne (SL) whch s the bass for far expected returns gven the covarance rsk of the asset f 1

2 ctve Portfolo anagement The SL defnes the α of a securty: E(r ) E(r ) 15.5% E(r ) 14% E(r ) 13% α ß 1 ß 1.3 ß Rsk ( E( r ) rf ) β [ E( r ) rf ] α ctve Portfolo anagement How should an nvestor decde to choose an actve or a passve strategy?

3 ctve Portfolo anagement ctve portfolo management If a manager has above average sklls n market tmng and/or stock (asset) pckng he can choose an actve strategy ost managers wll not beat the passve strategy (whch means nvestng the market ndex) but exceptonal (brght) managers can beat the average forecasts of the market There exst portfolo managers that produce abnormal returns that are beyond pure luck Objectve s to maxmze the CL (captal allocaton lne) ctve Portfolo anagement arket tmng example ssume an nvestor puts $1,000 n a 30-day commercal paper (rskless nstrument) on Jan 1, 197 and rolls t over and holds t untl Dec 31, 1978 for 5 years, the endng value s $3,600 $1,000 $3,600 5 yrs 3

4 ctve Portfolo anagement arket tmng example n nvestor puts $1,000 n the NYSE ndex on Jan 1, 197 and renvests all ts dvdends n that portfolo. The endng value of that portfolo on Dec 31, 1978 would be: $67,500 $1,000 $67,500 5 yrs Perfect market tmng s the ablty to tell exactly at the begnnng of each perod whch nvestment wll outperform the other Suppose the nvestor has perfect market tmng n every month by nvestng ether n CP or the ndex, whchever yelds the hghest return, the endng value after 5 years s $5.36 bllon! ctve Portfolo anagement arket tmng Per onth ll Equtes Perfect arket Tmer PT (Far Charge) verage Return 0,85%,58% 0,55% verage Excess Return 0,64%,37% 0,34% Standard Devaton 5,89% 3,8% 3,55% Skewness 0,4 4,8,84 Standard devaton of the perfect market tmer s not an approprate measure of rsk The perfect market tmer elmnates the left tal of the dstrbuton (return s skewed to the rght) 4

5 ctve Portfolo anagement arket tmng Perfect market tmng s not possble snce t requres perfect foresght The abnormal return of a perfect market tmer s not an addtonal rsk premum The perfect market tmer certanly wll charge a fee for hs abltes (the nvestor s left wth the net return) Standard devaton s not a good measure for quantfyng the rsk of market tmng Perfect foresght s equvalent to holdng a call opton on the equty poston ctve Portfolo anagement arket tmng as call opton r f r f On the bass of ths call opton the manager can calculate hs far prce for the servce of the opton (see erton (1981)) 5

6 ctve Portfolo anagement The Treynor-Black model assumes that the securty markets are nearly effcent ctve portfolo management s to select the msprced securtes whch are then added to the passve market portfolo whose means and varances are estmated by the nvestment management frm unt Only a subset of securtes are analyzed n the actve portfolo ctve Portfolo anagement Treynor Black model conssts of several steps Estmate the beta and resdual rsk of each analyzed securty (use sngle ndex model) Determne the expected return and abnormal return (.e., alpha) (degree of msprcng) Less the full dversfcaton comes from the msprced assets Determne the optmal weghts of the actve portfolo accordng to the estmated alpha, beta and resdual rsk of each securty Determne the optmal weghts of the the entre rsky portfolo (actve portfolo + passve market portfolo) 6

7 ctve Portfolo anagement Treynor Black model portfolo constructon Step 1 (forecast for passve portfolo has been made) r r + β ( r r ) + ε f f Step (estmate alpha for msprced securtes) r k r β ( r r ) + ε + α f k f msprcng Step 3 Group all securtes wth nonzero alpha nto a portfolo called actve portfolo. In ths portfolo, α, β and σ (ε ) are to be estmated. k k ctve Portfolo anagement Optmzaton process n the TB model Return New CL P. CL ( E( r ) rf ) β [ E( r ) rf ] + α Rsk 7

8 8 ctve Portfolo anagement We start out wth a portfolo (actve + passve) ean varance analyss results n an optmal weght P r w wr w r ) (1 ) ( + f r r E R R w + ) ( ) ( ) 1 ( * σ ε σ β α α ctve Portfolo anagement If we set n the beta-coeffcent equal to one, ß 1 we get oreover we get the followng relatonshp The slope for the CL s 0 ) ( R w σ ε σ α 0 0 * ) (1 1 w w w β + ) ( + P R S ε σ α σ Sharpe + Informaton Rato

9 ctve Portfolo anagement For each securty of the set of under- (over)prced ones we get the optmal weghts as w k n α / σ ( ε ) 1 k These optmal weghts have to be appled when the CL maxmzng portfolo s constructed We make use of the followng example k α / σ ( ε ) ctve Portfolo anagement We consder the followng example Stock lpha Beta Sgma lpha/sgma 1 7% 1,6 45% 0,1556-5% 1 3% -0, % 0,5 6% 0,1154 On the bass of these asset the portfolo s constructed (actve and passve) 9

10 ctve Portfolo anagement Wth the returns and unsystematc rsk we get Stock lpha Sgma Quotent Weght 1 7% 0,05 0,3457 1,1477-5% 0,104-0,4883-1,61 3 3% 0,0676 0,4438 1,4735 Sum 0,301 1,0000 The portfolo characterstcs are / lpha 0,56% w / 0.04 Beta 0,9519 * Rsk 0,687 w ( ) ctve Portfolo anagement Takng the optmal weghts for the actve and the passve portfolos together we get Stocks 1 Fnal Poston x , x(-1.61) -0, x ,03 ctve Portfolo 0,1495 Passve Portfolo 0,8505 Sum 1,0000 Performance of the overall portfolo s S S P P

11 Passve Portfolo anagement The nvestor s convnced that she cannot systematcally beat the market and nvests n the market portfolo Passve strateges are: Long term buy and hold strategy Indexcaton Replcaton of an ndex (market or specalzed) Samplng and trackng error strateges Portfolo rebalancng Passve Portfolo anagement Indexaton: Identfy an ndex as a benchmark for the strategy The followng ndexaton strateges exst Replcaton of benchmark (ndex) performance passve strategy never tres to outperform the benchmark The trackng error s a measure of accuracy for the passve strateges Trackng error s defned as ( R R ) R Pt Index return, R Bt Benchmark return TE N t 1 1 Pt N Bt 11

12 Passve Portfolo anagement lternatvely one can use the standard devaton of the resduals of an ndex model R Pt TE a P + b σ ( ε ) t P R Bt + ε t Ths measure dentfes the unsystematc rsk of the portfolo as the trackng error If the portfolo s as well dversfed as the benchmark ths rsk should be almost zero Passve Portfolo anagement Rebalancng strateges are an nstrument to fne tune a passve strategy Rebelancng s used to manage trackng error (f ndexng or not) to mantan a desred set of weghts or rsk level to accommodate the needs of a clent to react to changes n market rsk levels to counteract bankruptces, mergers, IPOs Rebalancng has a bg dsadvantage t can be very costly 1

13 Passve Portfolo anagement We explore the followng example of an equally weghted poston Jan. 1 Prce per Share Number of Shares Value % of Total Value Beta X $ Y 15 $ Z $ Total $ Passve Portfolo anagement fter 6 month the portfolo looks lke June 1 Prce per Share Number of Shares Value % of Total Value Beta down X $ % up 33% Y 0 $ unch. Z $ Total

14 Passve Portfolo anagement Because of the prce changes the portfolo s no longer equally weghted We need to rebalance Sell Y, buy X and Z Every sngle Postons must be reset to a value of 10445/3 348 Sell of Y (48 shares) Buy of X (51 shares) Buy of Z (4 shares) Passve Portfolo anagement fter rebalancng the portfolo looks lke June 1 Rebalanced Prce per Share Number of Shares $ Value % of Total Value Beta X $ Y 0 $ Z $ Total

15 Passve Portfolo anagement What are the consequences of ths rebalancng strategy? Rsk exposure of the ndvdual poston s the same Sngle asset has the same weght as before, only the total value of poston has changed Total rsk of the poston (measured n terms of beta) has been ncreased snce the rsk of the ndvdual postons has changed In an alternatve strategy the rsk of the portfolo s kept constant Passve Portfolo anagement We rebalance to establsh a target beta of 1. No unque soluton for more than securtes Need to sell hgh β stocks and buy low β stocks For example, sell Y, buy Z, hold X constant β p (.56)(1.3)+(W Y )(1.7)+(1-.56-W Y )(.8) Fnd Y such that β p 1. W Y.30 > W Z $3488 n X, $3151 n Y, $4611 n Z 15